Not able to downgrade to previous macOS

While you can install a macOS upgrade over itself (same version number and sub number), you can't go to an earlier version when you are still booted to the newer version. That is why you have to boot to Recovery (or boot from install media) and erase the startup volume and install the earlier version.

You can test it by booting from the install media. In any event, make sure you have a backup or two so you can at least go back to Monterey w/ all your information.

DId the Big Sur installer download w/o problems?

The link Old Toad supplies specifically said do not open

• Download: macOS Monterey, macOS Big Sur, macOS Catalina, macOS Mojave, or macOS High Sierra 
• These download to your Applications folder as an app named Install macOS [version name]. If the installer opens after downloading, quit it without continuing installation. To get the correct installer, download from a Mac that is using macOS Sierra 10.12.5 or later, or El Capitan 10.11.6. Enterprise administrators, please download from Apple, not a locally hosted software-update server. 

Then the instructions say

Use the 'createinstallmedia' command in Terminal

and give detailed instructions for using terminal commands.

You don't just copy it to the Flash Drive. You need to follow the instructions to use the Terminal with this command:

sudo /Applications/Install\ macOS\ Big\ Sur.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume

Open the Installer download app and look for the createinstallmedia file in the Resources folder of the App. Drag it into the Terminal right after "Resources/". Then enter space-- and drag the flash drive into the Terminal window. The flash drive must be named "MyVolume".

Create a bootable flash drive installer according to this Apple document: How to create a bootable installer for macOS - Apple Support (IN)

Boot with the Option key held down, select the installer and go from there.

Also you can't install a system older than the one that originally came with the Mac.

but when I downloaded Big Sur to my applications folder I got the error message and it wouldn’t open.

Yes, the Big Sur installer cannot install over the top of Monterey. It cannot run. That doesn't mean you can't make a bootable USB installer from it.